Geodesic
On Poincarje-Chetaev's equations
Theoretical and applied mechanics, Tome 20 (1994) no. 1, p. 189 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

The remarkable idea of II. Poincare to represent equations of motion of a holonomic system by means of some transitive Lie's group of infinitesimal transformations was generalized by N. Chetaev for the case of non-stationary constraints and of dependent variables with an intransitive group of virtual displacements. Chetaev has also proposed the canonical form and the generalized Hamilton-Jacobi equation for Poincare’s equations and proved the generalizations of the Poisson and Jacobi theorems. In the lecture I prove that in the general case the Poincare-Chetaev’s canonical equations are the Hamiltonian equations for the non-canonical formulation. It is also proved that the equations of motion of a system written in superfluous coordinates and that of Euler-Lagrange written in quasi-coordinates are the special forms of the Poincare-Chetaev’s equations. The question of using the Poincare-Chetaev’s equations for non-holonomic systems is also discussed. 
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Valentin V. Rumyantsev. On Poincarje-Chetaev's equations. Theoretical and applied mechanics, Tome 20 (1994) no. 1, p. 189 . http://geodesic.mathdoc.fr/item/TAM_1994_20_1_a15/